In how many ways can 6 lottery tickets be distributed among 4 different…

When n distinct items are distributed among k distinguishable recipients and each recipient may receive any number of items (including zero or more than one), every item independently has k choices of recipient — by the multiplication principle (rule of product), the total number of ways is kn. This is different from a permutation (nPr), which counts ordered selections of r items out of n with no repeats, and from a combination (nCr), which counts unordered selections.

Here n = 6 distinct lottery tickets and k = 4 distinguishable people, and each person can get any number of tickets (so a ticket's recipient can repeat across people). Ticket 1 can go to any of the 4 people, ticket 2 independently can go to any of the 4 people, and so on for all 6 tickets. Total ways = 4 × 4 × 4 × 4 × 4 × 4 = 46.

1. 6P4 = 6 × 5 × 4 × 3 = 360 only counts handing out 4 of the 6 tickets, one each, with no repeats — it silently drops 2 tickets and forbids any person from getting a second ticket, so it doesn't fit “any number of tickets.”

2. 6C4 = 15 counts ways to choose a subset of 4 tickets, without assigning them to specific people at all.

3. 64 = 1296 would be the answer only if there were 4 tickets and 6 people to receive them — the reverse of this problem.

4. So the option consistent with all six tickets being distributed and any person receiving any number of them is 46.

Therefore, the number of ways is 46.